Question

assignment: page 135
determine the measure of the unknown angle in each triangle.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°.

Step2: Solve for (a)

Let the unknown angle in triangle ABC be $\angle B$. We know $\angle A = 78^{\circ}$ and $\angle C=37^{\circ}$. Using the angle - sum property $\angle A+\angle B+\angle C = 180^{\circ}$. So, $\angle B=180^{\circ}-\angle A - \angle C=180^{\circ}-78^{\circ}-37^{\circ}=65^{\circ}$.

Step3: Solve for (b)

Let the unknown angle in triangle PQR be $\angle R$. We know $\angle P = 80^{\circ}$ and $\angle Q = 66^{\circ}$. Using the angle - sum property $\angle P+\angle Q+\angle R=180^{\circ}$. So, $\angle R=180^{\circ}-\angle P-\angle Q=180^{\circ}-80^{\circ}-66^{\circ}=34^{\circ}$.

Step4: Solve for (c)

Let the unknown angle in triangle KLM be $\angle L$. We know $\angle K = 35^{\circ}$ and $\angle M = 29^{\circ}$. Using the angle - sum property $\angle K+\angle L+\angle M = 180^{\circ}$. So, $\angle L=180^{\circ}-\angle K-\angle M=180^{\circ}-35^{\circ}-29^{\circ}=116^{\circ}$.

Step5: Solve for (d)

Let the unknown angle in triangle GHI be $\angle G$. We know $\angle H = 90^{\circ}$ and $\angle I = 32^{\circ}$. Using the angle - sum property $\angle G+\angle H+\angle I=180^{\circ}$. So, $\angle G=180^{\circ}-\angle H-\angle I=180^{\circ}-90^{\circ}-32^{\circ}=58^{\circ}$.

Answer:

(a) $65^{\circ}$
(b) $34^{\circ}$
(c) $116^{\circ}$
(d) $58^{\circ}$